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Longitudinal vibrations in circular rods: A systematic approach

Record type: Article

A systematic method is developed for expressing the frequency squared ?2 and the corresponding displacement fields of harmonic waves in a long thin rod as an even power series in qa, where q is the wavenumber along the rod and a is a representative transverse dimension. For longitudinal waves in a circular rod, the evaluation is reduced to algebraic recursion, giving coefficients analytically in terms of Poisson's ratio v, to many orders. The second nontrivial coefficient, corresponding to Rayleigh–Love theory in the present longitudinal case and Timoshenko theory in the flexural case, is thus put on a firm footing without reliance on ad hoc physical assumptions. The results are compared to available exact predictions, and shown to be accurate for moderate values of qa (5% accuracy for qa?1.5) with just two terms. Improvements based on the Rayleigh quotient guarantee positivity and the correct asymptotic power, and the variational principle further ensures that the accuracy improves monotonically with the order of approximation. With these features, accurate results are obtained for larger qa (5% accuracy for qa?3), so that results are valid for rods that are by no means thin. Application of these methods to the flexural case has been presented separately

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Citation

Stephen, N.G., Lai, K.F., Young, K. and Chan, K.T. (2012) Longitudinal vibrations in circular rods: A systematic approach Journal of Sound and Vibration, 331, (1), pp. 107-116. (doi:10.1016/j.jsv.2011.08.021).

More information

Published date: January 2012
Organisations: Computational Engineering & Design Group

Identifiers

Local EPrints ID: 197439
URI: http://eprints.soton.ac.uk/id/eprint/197439
ISSN: 0022-460X
PURE UUID: d1138c95-4e45-4a8b-ac4f-870c833127a4

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Date deposited: 23 Sep 2011 10:12
Last modified: 18 Jul 2017 11:20

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Contributors

Author: N.G. Stephen
Author: K.F. Lai
Author: K. Young
Author: K.T. Chan

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